Torque Measurement

NOTE 14: I've never gone into any detail on the torque measurement
scheme employed in the Club Scout. Since Prof. Steve Day published his
article in the recent PCS Journal the cat is out of the bag.

I took Dynacraft's three day course on Advanced Shaft Technology several
years ago. We were introduced to their fitting equation called DSFI.
In this equation the shaft's frequency and torque are related to the
golfer's swing speed. The equation includes a fifth root of torque term.
Since torque is usually a small number greater than one its fifth root
will always be a number a bit larger than one. I didn't think therefore
that torque was a very important term in fitting a set of clubs. I had
my calculator with me and I started to punch in a few numbers to see
the effect of torque. Much to my surprise a degree change in torque
results in nearly a 10 cpm change in desired frequency for a given swing
speed. If their formula is reasonable then torque is indeed a very important
factor in fitting and since graphite shaft torque varies all over the
map it seemed to me I should look into a way of measuring it.

To measure torque the first thing is to clamp the butt of the shaft.
Since my frequency analyzer already has a clamp I tried to come up with
a scheme that made use of it. Torque is normally measured statically.
That is, clamp the butt and see how much the shaft twists when one foot
pound of torque is applied to the tip. At first I thought I could use
my Club Scout electronics unit as a simple support for the tip of the
shaft. I then would clamp a one foot arm at right angles to the tip
of the shaft and measure the deflection when a one pound weight was
added to the end of this arm. I thought about using protrators or clubmaker's
levels to measure the angle. This would only give accuracy to a half
a degree or so and I thought it would be nice to get down to a tenth.
I decided to attach a laser diode to the hub of the arm that clamps
to the shaft. The laser would be projected onto a ruler some distance
away. When the weight was added the displacement of the laser beam on
the ruler could then be measured and the torque angle computed. This
worked very well and accuracies to a few hundredths of a degree could
be obtained. While running these tests I noticed the arm oscillate up
and down when I added the one pound weight. Just for the heck of it
I measured its frequency with a Club Scout I. I distinctly remember
it came up 411. I gave the rod a bounce and again read 411. After about
a dozen 411's I got real intrigued. I then took an assortment of shafts
I had over a range of torques. I measured the torques with the laser
and also recorded the frequency. I plotted one against the other and
got a very smooth curve. At this point I blew the dust off of my old
college Dynamics text book. I looked up the formula for torsional frequency
and found it was inversely proportional to the square root of the torque
and the moment of inertia of the torsion arm attached to the shaft.
I computed the moment of inertia of my torsion arm and plugged the frequency
numbers into the equation and was able to compute torques that matched
the laser measurements within about a tenth of a degree. This meant
I could accurately determine torque by just measuring the arm's vibration
frequency.

When I built an actual torsion arm to be used with a Club Scout I designed
it to have a moment of inertia such that the frequencies would be in
the 200 to 300 cpm region. This was done because the analyzer was designed
to produce its best accuracies in this region. I have gone through about
five iterations in torsion arm design but they all have exactly the
same moment of inertia. The changes were made simply to make it easier
to produce.

Moment of inertia is defined as mass times length squared. This means
the weight can be fairly light if the arm's length is long. To compute
moment of inertia a bit a calculus is needed, fortunately that old Dynamics
book of mine had the equations listed for a whole bunch of different
shapes. This made life a lot easier for me. Virtually all of the inertia
is the result of the weight on the end of the torsion bar. The hub and
the steel rod contribute virtually nothing.